A car of mass 60kg is moving on a road at 30m/s. Suddenly put in neutral gear, after that its speed decreases due to air drag and other resistance forces as v=30/(1+t/10)m/s. Choose the correct statement.
A. Car is uniformly accelerated in neutral gear.
B. Magnitude of acceleration of car is 1m/s^2 when its speed becomes 10m/s.
C. Sum of all the resistance forces acting on car when its speed becomes 15m/s is 45N.
D. Power needed to move the car at 10m/s is 100 watt
Plz answer ASAP its urgent
Answers
Given : A car of mass 60kg is moving on a road at 30m/s.
Suddenly put in neutral gear, after that its speed decreases due to air drag and other resistance forces as v=30/(1+t/10)m/s.
To Find :
Choose the correct statement.
A. Car is uniformly accelerated in neutral gear.
B. Magnitude of acceleration of car is 1m/s^2 when its speed becomes 10m/s.
C. Sum of all the resistance forces acting on car when its speed becomes 15m/s is 45N.
D. Power needed to move the car at 10m/s is 100 watt
Solution :
m = 60 kg
u = 30 m/s
v=30/(1+t/10)
at t = 0 , v = 0
=> 30 = 30 / ( 1 + 0/10)
=> 30 = 30/1
=> 30 = 30 Verified
v=30/( 1 +t/10) = 300/(10 + t)
dv/dt = -300/(10 + t)²
a = -300/(10 + t)²
Acceleration is not uniform
Car is uniformly accelerated in neutral gear. INCORRECT
v=30/(1+t/10)
v = 10
=> 10 = 30/(1 + t/10)
=> 1 + t/10 = 3
=> t/10 = 2
=> t = 20
a = -300/(10 + t)² = -300/( 10 + 20)² = -1/3 m/s²
Magnitude of acceleration of car is -1/3 m/s² when its speed becomes 10 m/s.
Hence Magnitude of acceleration of car is 1 m/s² when its speed becomes 10 m/s is INCORRECT
v = 15
=> => 15 = 30/(1 + t/10)
=> 1 + t/10 = 2
=> t/10 = 1
=> t = 10
a = -300/(10 +10)² = -300/( 10 + 10)² = -3/4 m/s²
F = ma = 60 * (-3/4) = -45 N ( -ve sign shows opposite force )
Sum of all the resistance forces acting on car when its speed becomes 15 m/s is, 45 N. - CORRECT
v = 10 m/s at 20 secs
a = -1/3 m/s²
F = ma = 60 (-1/3) = -20N
Hence 20N force v = 10 m/s
20 * 10 = 200 W
Power needed to move the car at 10 m/s is, 100 watt. is INCORRECT
Sum of all the resistance forces acting on car when its speed becomes 15 m/s is, 45 N. - CORRECT
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